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     "source": [
      "Kalman filtering\n",
      "======================================================================\n",
      "\n",
      "This is code implements the example given in pages 11-15 of [An\n",
      "Introduction to the Kalman\n",
      "Filter](https://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf) by Greg\n",
      "Welch and Gary Bishop, University of North Carolina at Chapel Hill,\n",
      "Department of Computer Science."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Kalman filter example demo in Python\n",
      "\n",
      "# A Python implementation of the example given in pages 11-15 of \"An\n",
      "# Introduction to the Kalman Filter\" by Greg Welch and Gary Bishop,\n",
      "# University of North Carolina at Chapel Hill, Department of Computer\n",
      "# Science, TR 95-041,\n",
      "# https://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf\n",
      "\n",
      "# by Andrew D. Straw\n",
      "\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "plt.rcParams['figure.figsize'] = (10, 8)\n",
      "\n",
      "# intial parameters\n",
      "n_iter = 50\n",
      "sz = (n_iter,) # size of array\n",
      "x = -0.37727 # truth value (typo in example at top of p. 13 calls this z)\n",
      "z = np.random.normal(x,0.1,size=sz) # observations (normal about x, sigma=0.1)\n",
      "\n",
      "Q = 1e-5 # process variance\n",
      "\n",
      "# allocate space for arrays\n",
      "xhat=np.zeros(sz)      # a posteri estimate of x\n",
      "P=np.zeros(sz)         # a posteri error estimate\n",
      "xhatminus=np.zeros(sz) # a priori estimate of x\n",
      "Pminus=np.zeros(sz)    # a priori error estimate\n",
      "K=np.zeros(sz)         # gain or blending factor\n",
      "\n",
      "R = 0.1**2 # estimate of measurement variance, change to see effect\n",
      "\n",
      "# intial guesses\n",
      "xhat[0] = 0.0\n",
      "P[0] = 1.0\n",
      "\n",
      "for k in range(1,n_iter):\n",
      "    # time update\n",
      "    xhatminus[k] = xhat[k-1]\n",
      "    Pminus[k] = P[k-1]+Q\n",
      "    \n",
      "    # measurement update\n",
      "    K[k] = Pminus[k]/( Pminus[k]+R )\n",
      "    xhat[k] = xhatminus[k]+K[k]*(z[k]-xhatminus[k])\n",
      "    P[k] = (1-K[k])*Pminus[k]\n",
      "\n",
      "plt.figure()\n",
      "plt.plot(z,'k+',label='noisy measurements')\n",
      "plt.plot(xhat,'b-',label='a posteri estimate')\n",
      "plt.axhline(x,color='g',label='truth value')\n",
      "plt.legend()\n",
      "plt.title('Estimate vs. iteration step', fontweight='bold')\n",
      "plt.xlabel('Iteration')\n",
      "plt.ylabel('Voltage')\n",
      "\n",
      "plt.figure()\n",
      "valid_iter = range(1,n_iter) # Pminus not valid at step 0\n",
      "plt.plot(valid_iter,Pminus[valid_iter],label='a priori error estimate')\n",
      "plt.title('Estimated $\\it{\\mathbf{a \\ priori}}$ error vs. iteration step', fontweight='bold')\n",
      "plt.xlabel('Iteration')\n",
      "plt.ylabel('$(Voltage)^2$')\n",
      "plt.setp(plt.gca(),'ylim',[0,.01])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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iIiJSMYY1IiIiFdFqtUhISDB3MUhFGNaIiIhUJDMzEz4+PuYuBv1/wcHBWLZsmVnLwLBG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\nEdYAAABs7H/HgjejrTuPLQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x24fe190>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1uuSSS/TGG29o3759uu+++4JZV7NAyAMAAHZpcsibOnWqYmNjNXToUF122WVq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\nAAAQgQh5AAAAEYiQBwAAEIH+P5xCzN97d2rJAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x266af90>"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}
